Respuesta :
Answer:
[tex]8.3\cdot 10^{22}[/tex] photons
Explanation:
The energy of a photon is given by
[tex]E_1 = \frac{hc}{\lambda}[/tex]
where
[tex]h=6.63\cdot 10^{-34} Js[/tex] is the Planck constant
[tex]c=3.0\cdot 10^8 m/s[/tex] is the speed of light
[tex]\lambda[/tex] is the photon wavelength
Here we have
[tex]\lambda=1.5\cdot 10^{-6} m[/tex]
So, the energy of 1 of these infrared photons is
[tex]E_1=\frac{(6.63\cdot 10^{-34})(3\cdot 10^8)}{1.5\cdot 10^{-6}}=1.32\cdot 10^{-19} J[/tex]
The amount of energy needed to increase the temperature of the cup of water is:
[tex]E=mC\Delta T[/tex]
where
m = 175 g is the mass
[tex]C=4.186 J/gC[/tex] is the specific heat capacity
[tex]\Delta T=40-25=15^{\circ}C[/tex] is the increase in temperature
So,
[tex]E=(175)(4.186)(15)=10,988 J[/tex]
Therefore, the number of photons needed is:
[tex]n=\frac{E}{E_1}=\frac{10,988}{1.32\cdot 10^{-19}}=8.3\cdot 10^{22}[/tex]
The number of photons required is [tex]8.3*10^{22}[/tex].
The total energy required to raise the temperature of water from 25.0°C to 40°C will be provided by the energy carried by the photons.
The energy required to raise the temperature of water from 25.0°C to 40°C will be:
ΔQ = mcΔT
where, m = mass of water = 175 g (given)
c = specific heat capacity of water = 4.186 J/g°C
ΔT = change in temperature = 40 - 25 = 15°C
ΔQ = 175 × 4.186 × 15 = 10988.25 J
So the photos must provide ΔQ amount of energy.
The energy carried by one photon:
E = hc/λ
where, h = Planck's constant, c = speed of light and λ = wavelength of photon = [tex]1.5*10^{-6}[/tex] m
[tex]E = \frac{6.626*10^{-34}*3*10^{8} }{1.5*10^{-6} }[/tex] = [tex]13.252*10^{-20}[/tex]
No of photons needed to produce ΔQ amount of energy:
n = ΔQ / E = [tex]\frac{10988.25}{13.252*10^{-20}}[/tex]
n = [tex]8.3*10^{22}[/tex], is the number of photons required.
Learn more about Infrared Radiation:
https://brainly.com/question/20779091?referrer=searchResults
